On 9 Jan 2002, at 10:40, Tim May wrote:
By the way, for all of you who struggled to understand Godel's Theorem expressed in the "logic" formulation that Godel first used--and that was the basis of Newman's fairly popular exposition--there are very understandable formulations of Godel's Theorem in terms of information theory and compressibility. Chaitin has a very clean one (no Kleene pun intended).
Maybe I'm oversimplifying, but it seems to me that Godel's theorem follows trivilaly once you've heard of Cantor's diagonal slash. As I understand it, Godel's theorem says in essence that in any system complex enough to include the irrational numbers there must be statements which are true in that system but which cannot be proven in that sytem. But since there are uncountably many irrational numbers, there are uncountably many statements of the form A=A which are true but which cannot be expressed with a finite number of symbols. George
--Tim May
George